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针对一类切换奇异时滞系统,对其容许性问题进行了研究。基于时滞区间分割的思想,构造一类新型的多Lyapunov泛函。利用推广的Lyapunov稳定性理论,通过引入适当的自由权矩阵,在设计的切换律下,得到了基于严格线性矩阵不等式表示的自治切换奇异时滞系统是容许的时滞依赖充分条件;通过设计相应的状态反馈子控制器,给出了保证闭环切换奇异时滞系统是容许的时滞依赖充分条件,同时给出了各子控制器的显式表达式。最后,数值算例表明该方法的可行性和有效性。
For a class of switched singular time-delay systems, the admissibility problems are studied. Based on the idea of interval partitioning with time delay, a new type of multi-Lyapunov functional is constructed. By using the generalized Lyapunov stability theory and by introducing the appropriate free-weight matrix, the singular time-delay system of autonomy switching based on strict linear matrix inequalities is obtained under the switching law of design. State feedback sub-controller is given, and sufficient conditions for the delay-dependent delay-dependent singular time-delay system to be guaranteed are given. Explicit expressions of each sub-controller are also given. Finally, numerical examples show the feasibility and effectiveness of the proposed method.